Information on Result #3178345
Digital (33, 57, 549)-net over F81, using 1 times m-reduction based on digital (33, 58, 549)-net over F81, using
- net defined by OOA [i] based on linear OOA(8158, 549, F81, 25, 25) (dual of [(549, 25), 13667, 26]-NRT-code), using
- OOA 12-folding and stacking with additional row [i] based on linear OA(8158, 6589, F81, 25) (dual of [6589, 6531, 26]-code), using
- discarding factors / shortening the dual code based on linear OA(8158, 6591, F81, 25) (dual of [6591, 6533, 26]-code), using
- construction X applied to C([0,12]) ⊂ C([0,7]) [i] based on
- linear OA(8149, 6562, F81, 25) (dual of [6562, 6513, 26]-code), using the expurgated narrow-sense BCH-code C(I) with length 6562 | 814−1, defining interval I = [0,12], and minimum distance d ≥ |{−12,−11,…,12}|+1 = 26 (BCH-bound) [i]
- linear OA(8129, 6562, F81, 15) (dual of [6562, 6533, 16]-code), using the expurgated narrow-sense BCH-code C(I) with length 6562 | 814−1, defining interval I = [0,7], and minimum distance d ≥ |{−7,−6,…,7}|+1 = 16 (BCH-bound) [i]
- linear OA(819, 29, F81, 9) (dual of [29, 20, 10]-code or 29-arc in PG(8,81)), using
- discarding factors / shortening the dual code based on linear OA(819, 81, F81, 9) (dual of [81, 72, 10]-code or 81-arc in PG(8,81)), using
- Reed–Solomon code RS(72,81) [i]
- discarding factors / shortening the dual code based on linear OA(819, 81, F81, 9) (dual of [81, 72, 10]-code or 81-arc in PG(8,81)), using
- construction X applied to C([0,12]) ⊂ C([0,7]) [i] based on
- discarding factors / shortening the dual code based on linear OA(8158, 6591, F81, 25) (dual of [6591, 6533, 26]-code), using
- OOA 12-folding and stacking with additional row [i] based on linear OA(8158, 6589, F81, 25) (dual of [6589, 6531, 26]-code), using
Mode: Constructive and linear.
Optimality
Show details for fixed k and m, k and s, k and t, m and s, m and t, t and s.
Other Results with Identical Parameters
None.
Depending Results
None.